5-4 Inverses, Contrapositives, and Indirect Reasoning

# 5-4 Inverses, Contrapositives, and Indirect Reasoning - The...

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Inverses, Contrapositives, and Indirect Reasoning Section 5-4

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negation – the denial of a statement Ex. “An angle is obtuse.” Negation – “An angle is not obtuse.”
Inverse ~p ~q An inverse statement can be formed by negating both the hypothesis and conclusion. If it is an apple, then it is a fruit. Inverse: If it is not an apple, then it is not a fruit. The inverse may be true or false.

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Contrapositive ~q ~p A contrapositive is formed by negating the hypothesis and conclusion of the converse. If it is an apple, then it is a fruit. Contrapositive : If it is not a fruit, then it is not an apple.

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Unformatted text preview: The contrapositive of a true conditional is true and of a false conditional is false. Steps for Writing an Indirect Proof 1. Assume the conclusion is false. 2. Show that this assumption leads to a contradiction of the hypothesis, or some other fact, such as a definition, postulate, theorem, or corollary. 3. Point out that because the false conclusion leads to an incorrect statement, the original conclusion must be true. Joke Time What did the cloud say to the banker? I need a rain check. What did the cloud have under its raincoat? Thunderwear...
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5-4 Inverses, Contrapositives, and Indirect Reasoning - The...

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